The presence of shear bands in flow or strain localisation have been studied extensively in the past, both experimentally and in computer simulations, in soft glassy materials and hard glasses, as described in Ref. [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. In the context of hard glasses, strain localisation has been observed and discussed in the context of yielding, as already mentioned several times. Apart from the work mentioned above, there have been some observations, starting from [11]}, that a correlation exists with the annealing of glasses and strain localisation during yield. However, a physical understanding of the connection is only now beginning to emerge. On the other hand, one may also inquire as to whether the strain localisation observed at yielding will persist or the shear band will grow and engulf the system as the strain increases. In the rheological context of mainly soft glasses, the persistence or otherwise of shear bands, and dependence on shear rates and other parameters, have been analysed by a variety of investigations [12]}, [13]}, [14]}, [15]}, [16]}, [8]}, [18]}, [9]}, [20]}. The physical picture of the theoretical analyses invoke some form of competition between rates of aging, which is treated as a spontaneous process, and rejuvenation, which is often associated with shearing. Following Coussot and Ovarlez [13]}, Martens et al [15]} analysed a related mechanism, where the relaxation time taken by an activated region to relax stresses plays a key role (refer to Figure REF ). When this time scale \(\tau _{el}\)  gets long enough, permanent shear bands arise. In a mean field calculation, this can be seen in non-monotonic flow curves (Figure REF ) and in a simulation, in the form of localisation of shear. In the latter case, shear banding is observed only when an Eshelby-type stress propagator is used but not when a short range propagator is used. This latter observation seems to support the idea that the nature of stress propagation is of key importance, as in the analysis in Ref. [23]}, [24]}. But once again, mean field or other abstract models [15]}, [16]} appear to capture shear banding even without explicit consideration of the nature of stress propagation in space. Further, aging and rejuvenation rates are not available when one considers AQS dynamics, and where the effects of annealing appear in the rheological models is also not clear. In the context of cyclic shear discussed above, even though performed under AQS conditions, aging and rejuvenation effects are present and play a role, but a key difference from some of the model studies mentioned is that both aging and rejuvenation are induced by the shear deformation itself, heterogeneously in space. It would be interesting to have theoretical analyses that will encompass these scenarios.
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